Gaussian expansions and bounds for the Poisson distribution applied to the Erlang B formula

Janssen, Ajem Guido; Leeuwaarden, Johan S. H. van; Zwart, Bert

doi:10.1017/s0001867800002408

Cited by 23 publications

(30 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, we take a different approach, aiming for new asymptotic expansions for the probability of delay and the probability of rejection. The first terms of these expansions are the QED limits, and the higherorder terms are refinements to these QED limits for finite s. This generalizes earlier results on the Erlang B, C and A models [JvLZ08,JvLZ11,ZvLZ12].…”

Section: Introductionsupporting

confidence: 82%

Scaled control in the QED regime

Janssen

Leeuwaarden

Sanders

2013

Performance Evaluation

View full text Add to dashboard Cite

We develop many-server asymptotics in the Quality-and-Efficiency-Driven (QED) regime for models with admission control. The admission control, designed to reduce the incoming traffic in periods of congestion, scales with the size of the system. For a class of Markovian models with this scaled control, we identify the QED limits for two stationary performance measures. We also derive corrected QED approximations, generalizing earlier results for the Erlang B, C and A models. These results are useful for the dimensioning of large systems equipped with an active control policy. In particular, the corrected approximations can be leveraged to establish the optimality gaps related to square-root staffing and asymptotic dimensioning with admission control.

show abstract

Section: Introductionsupporting

confidence: 82%

Scaled control in the QED regime

Janssen

Leeuwaarden

Sanders

2013

Performance Evaluation

View full text Add to dashboard Cite

show abstract

“…The normalized price is given by the Erlang-B function, which has been well studied in teletraffic theory. In particular upper and lower bounds are obtained in [13,17], and it is demonstrated in [16] that for a given arrival load λ, the Erlang-B function (hence, the break-even price) is a convex function of the capacity C, as can be observed from Figure 2(a). It is also worth noting that as the network capacity increases, the value of the break-even price at the critical load where λ = C decreases as demonstrated in Figure 2 significant margin), the break-even price is substantially lower than the primary price.…”

Section: Optimal Coordinated Access Policy a Profitabilitymentioning

confidence: 93%

Competition in Private Commons: Price War or Market Sharing?

Kavurmacioglu

Alanyali

Starobinski

2016

IEEE/ACM Trans. Networking

View full text Add to dashboard Cite

Abstract-This paper characterizes the outcomes of secondary spectrum markets when multiple providers compete for secondary demand. We study a competition model in which each provider aims to enhance its revenue by opportunistically serving a price dependent secondary demand, while also serving dedicated primary demand. We consider two methodologies for sharing spectrum between primary and secondary demand: In coordinated access, spectrum providers have the option to decline a secondary access request if that helps enhance their revenue. We explicitly characterize a break-even price such that profitability of secondary access provision is guaranteed if secondary access is priced above the break-even price, regardless of the volume of secondary demand. Consequently, we establish that competition among providers that employ optimal coordinated access leads to a price war, as a result of which the provider with the lowest break-even price captures the entire market. This result holds for arbitrary secondary demand functions. In uncoordinated access, primary and secondary users share spectrum on equal basis, akin to ISM bands. Under this policy, we characterize a market sharing price which determines a provider's willingness to share the market. We show an instance where the market sharing price is strictly greater than the break-even price, indicating that market equilibrium in an uncoordinated access setting can be fundamentally different as it opens up the possibility of providers sharing the market at higher prices.

show abstract

“…Examples for s = 10 and s = 20 are depicted in Figures 2 and 3, respectively. In the present study we refrain from using the bounds for inversion purposes, since the asymptotic inversion introduced in §5 already leads to highly accurate results in the case λ < s. Bounds similar to but sharper than (5.10) and (5.11) can be found in [10].…”

Section: B(s λ)mentioning

confidence: 93%

Asymptotic Inversion of the Erlang B Formula

Leeuwaarden¹,

Temme²

2009

SIAM J. Appl. Math.

Self Cite

View full text Add to dashboard Cite

The Erlang B formula represents the steady-state blocking probability in the Erlang loss model or M/M/s/s queue. We derive asymptotic expansions for the offered load that matches, for a given number of servers, a certain blocking probability. In addressing this inversion problem we make use of various asymptotic expansions for the incomplete gamma function. A similar inversion problem is investigated for the Erlang C formula.

show abstract

Gaussian expansions and bounds for the Poisson distribution applied to the Erlang B formula

Cited by 23 publications

References 16 publications

Scaled control in the QED regime

Scaled control in the QED regime

Competition in Private Commons: Price War or Market Sharing?

Asymptotic Inversion of the Erlang B Formula

Contact Info

Product

Resources

About